Question

question 2 - 3
click to match each property to all the quadrilaterals it applies to. there may be more than one quadrilateral selected for each row.
isosceles trapezoid parallelogram rhombus
opposite sides are always congruent
opposite angles are always congruent
all sides are always congruent
diagonals are always congruent

Explanation:

Opposite sides are always congruent

• Isosceles Trapezoid: In an isosceles trapezoid, only the non - parallel sides (the legs) are congruent. The parallel sides (bases) are not necessarily congruent. So, this property does not apply.
• Parallelogram: By the definition of a parallelogram, opposite sides are congruent.
• Rhombus: A rhombus is a special type of parallelogram. Since in a parallelogram opposite sides are congruent, and a rhombus has all the properties of a parallelogram, opposite sides of a rhombus are congruent.

Opposite angles are always congruent

• Isosceles Trapezoid: In an isosceles trapezoid, base angles are congruent. But opposite angles (non - base angles) are supplementary (sum to \(180^{\circ}\)) and not congruent.
• Parallelogram: In a parallelogram, opposite angles are congruent.
• Rhombus: A rhombus is a parallelogram. So, it has the property that opposite angles are congruent.

All sides are always congruent

• Isosceles Trapezoid: In an isosceles trapezoid, only the non - parallel sides (legs) are congruent. The bases are not congruent.
• Parallelogram: In a general parallelogram, adjacent sides are not necessarily congruent. Only opposite sides are congruent.
• Rhombus: By the definition of a rhombus, all four sides are congruent.

Diagonals are always congruent

• Isosceles Trapezoid: In an isosceles trapezoid, the diagonals are congruent.
• Parallelogram: In a general parallelogram, the diagonals bisect each other but are not necessarily congruent.
• Rhombus: In a rhombus, the diagonals are perpendicular bisectors of each other but are not necessarily congruent.

Answer:

Property	Isosceles Trapezoid	Parallelogram	Rhombus
Opposite angles are always congruent		\(\checkmark\)	\(\checkmark\)
All sides are always congruent			\(\checkmark\)
Diagonals are always congruent	\(\checkmark\)